N. Y. Chiang, R. Huang and V. M. Zavala, An Augmented Lagrangian Filter Method for Real-Time Embedded Optimization, IEEE Transactions on Automatic Control, vol. 62, no. 12, pp. 6110-6121, DOI: 10.1109/TAC.2017.2694806.
We present a filter line-search algorithm for nonconvex continuous optimization that combines an augmented Lagrangian function and a constraint violation metric to accept and reject steps. The approach is motivated by real-time optimization applications that need to be executed on embedded computing platforms with limited memory and processor speeds. The proposed method enables primal-dual regularization of the linear algebra system that in turn permits the use of solution strategies with lower computing overheads. We prove that the proposed algorithm is globally convergent and we demonstrate the developments using a nonconvex real-time optimization application for a building heating, ventilation, and air conditioning system. Our numerical tests are performed on a standard processor and on an embedded platform. We demonstrate that the approach reduces solution times by a factor of over 1000.